Abstract

Mathematical optimization plays a fundamental role in solving many problems in computer vision (e.g., cameracalibration, image alignment, structure from motion). It isgenerally accepted that second order descent methods are the most robust, fast, and reliable approaches for nonlinear optimization of a general smooth function. However, in thecontext of computer vision, second order descent methods have two main drawbacks: 1) the function might not be an-alytically differentiable and numerical approximations areimpractical, and 2) the Hessian may be large and not posi-tive definite. Recently, Supervised Descent Method (SDM),a method that learns the “weighted averaged gradients” in a supervised manner has been proposed to solve these issues. However, SDM is a local algorithm and it is likelyto average conflicting gradient directions. This paper proposes Global SDM (GSDM), an extension of SDM that divides the search space into regions of similar gradient direc-tions. GSDM provides a better and more efficient strategyto minimize non-linear least squares functions in computervision problems. We illustrate the effectiveness of GSDMin two problems: non-rigid image alignment and extrinsiccamera calibration.